True or False equation X = a ... ?

• December 23rd 2009, 09:47 AM
r-soy
True or False equation X = a ... ?
Hi all

1 : True or False and why ? : Equation X = a defines a function with independent variable X ?

2 : what the vertex of the parabola y= 1/2(x+3)^2 + 8 is ?

3 - the graph of exponential function f(x) = b^x where b>0 and b dont = 1 will pass through :

a) - (0,0) b) - (1,1 ) c) - ( 0,1 ) d) - (0,1)

I don't want the answer only also I need to explain the solving

thanks
• December 23rd 2009, 10:11 AM
skeeter
Quote:

Originally Posted by r-soy
Hi all

1 : True or False and why ? : Equation X = a defines a function with independent variable X ?

what does the graph of "x = a" look like? does it pass the vertical line test for a function?

2 : what the vertex of the parabola y= 1/2(x+3)^2 + 8 is ?

y = a(x-h)^2 + k has its vertex at (h,k)

3 - the graph of exponential function f(x) = b^x where b>0 and b dont = 1 will pass through :

a) - (0,0) b) - (1,1 ) c) - ( 0,1 ) d) - (0,1)

f(0) = b^0 = ?

I don't want the answer only also I need to explain the solving

thanks

...
• December 23rd 2009, 11:32 AM
r-soy
Hi skeeter I don't understand number 3 clearly is it possible explain more
• December 23rd 2009, 11:50 AM
skeeter
Quote:

Originally Posted by r-soy
Hi skeeter I don't understand number 3 clearly is it possible explain more

$\left(\frac{1}{3}\right)^0 = 1$

$\left(\frac{1}{2}\right)^0 = 1$

$2^0 = 1$

$3^0 = 1$

if $b > 0$ and $b \ne 1$ , then $b^0 =$ ?
• December 24th 2009, 01:50 AM
HallsofIvy
Quote:

Originally Posted by r-soy
Hi all

3 - the graph of exponential function f(x) = b^x where b>0 and b dont = 1 will pass through :

a) - (0,0) b) - (1,1 ) c) - ( 0,1 ) d) - (0,1)

I don't want the answer only also I need to explain the solving

thanks

$b^x$ is never equal to 0. Can you solve $b^1= 1$?
c) and d) appear to be the same! Are you sure you copied the problem correctly?
• December 24th 2009, 02:18 AM
r-soy
Quote:

Originally Posted by HallsofIvy
$b^x$ is never equal to 0. Can you solve $b^1= 1$?
c) and d) appear to be the same! Are you sure you copied the problem correctly?

yes.